
The connection between mathematics and
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used in the design of Gothic cathedrals, Rose windows,
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and awardwinning sculptors have used topology as the
basis for their pieces. Dutch artist M.C. Escher represented
infinity, Möbius ands, tessellations, deformations,
reflections, Platonic solids, spirals, symmetry, and
the hyperbolic plane in his works.
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Home > JeanFrancois Colonna :: A Gateway Between Art and Science

Last additions  JeanFrancois Colonna :: A Gateway Between Art and Science 
"Doubly Impossible Staircase," by JeanFrancois Colonna (Centre de Mathematiques Appliquees, Ecole Polytechnique)Traversing along the outside, the stairs always rise; but traversing along the inside, they always descend. Finally, alternating between the exterior and interior, it behaves like a normal staircase.  JeanFrancois ColonnaJun 20, 2008


"Artistic View of the Klein Bottle," by JeanFrancois Colonna (Centre de Mathematiques Appliquees, Ecole Polytechnique)In mathematics, the Klein Bottle is a nonorientable surface, i.e. a surface with no distinct "inner" or "outer" sides. Other related nonorientable objects include the Mobius strip and the real projective plane. Whereas a Mobius strip is a twodimensional object with one side and one edge, a Klein bottle is a threedimensional object with one side and no edges.Jun 16, 2008


"Bidimensional Visualization of the Verhulst Dynamics," by JeanFrancois Colonna (Centre de Mathematiques Appliquees, Ecole Polytechnique)In this image, grey, orange, and red represent negative Lyapunov exponents; yellow, green, and blue represent positive Lyapunov exponents. The two groups of colors distinguish stable systems from chaotic ones.Jun 16, 2008


"Artistic View of a Bidimensional Texture," by JeanFrancois Colonna (Centre de Mathematiques Appliquees, Ecole Polytechnique)This image was obtained by means of a selftransformation of a fractal process.Jun 16, 2008


"Clover51," by JeanFrancois Colonna (Centre de Mathematiques Appliquees, Ecole Polytechnique)This image shows the lack of associativity for addition and multiplication inside a computer. In order to be able to obtain the exact same results over the years for a certain computation, I did include the definition of some "devices" in my own programming language, which allow the definition of the precise order of the arithmetic operations: +, , *, and / (by the way, parentheses won't do that, for example, X=A+(B+C) does not mean T=B+C then X=A+T).
This opens the door to something very powerful: The possibility to dynamically redefine the arithmetic used when launching a program. This picture and "Clover52" are the results of the combination of eight elementary pictures: 3clover, 4clover, ... ,10clover with substitutions like (A+B) > MAX (A,B), (A*B) > (A+B).Jun 16, 2008


"Clover52," by JeanFrancois Colonna (Centre de Mathematiques Appliquees, Ecole Polytechnique)This image shows the lack of associativity for addition and multiplication inside a computer. In order to be able to obtain the exact same results over the years for a certain computation, I did include the definition of some "devices" in my own programming language, which allow the definition of the precise order of the arithmetic operations: +, , *, and / (by the way, parentheses won't do that, for example, X=A+(B+C) does not mean T=B+C then X=A+T).
This opens the door to something very powerful: The possibility to dynamically redefine the arithmetic used when launching a program. This picture and "Clover51" are the results of the combination of eight elementary pictures: 3clover, 4clover, ... ,10clover with substitutions like (A+B) > MAX (A,B), (A*B) > (A+B).Jun 16, 2008



